There is great interest in finding strong, fast nonlinear optical processes in semiconductors that are effective at pump frequencies in the near infrared. In recent years, progress has been made in identifying and understanding a number of strong free carrier mechanisms that operate at longer wavelengths, near 10.mu.. These processes can product large third order optical nonlinearities with relaxation times in the picosecond range. Third order nonlinear susceptibilities exceeding 10.sup.-6 esu with picosecond relaxation times have been observed. Unfortunately, most of these mechanisms have proven unsuitable for use at wavelengths in the 1.55.mu. range. They fail to make the transition from 10.mu. to 1.55.mu. either because the nonlinearity is too small at shorter wavelengths to be useful, or because the mechanism relies upon a pump photon resonance that cannot be extended to the 1.55.mu. spectral range. The 1.55.mu. wavelength is crucial for long distance optical communication applications, because at this wavelength optical fibers have zero dispersion, thus enabling digital optical signals to travel long distance without broadening.
The valley-transfer mechanism potentially can overcome these shortcomings and produce a strong, fast nonlinearity in the near infrared. The valley-transfer mechanism is described, for example, in an article by K. Kash et al, entitled "Nonlinear optical studies of picosecond relaxation times of electrons in n-GaAs and n-GaSb" in Applied Physics Letters, volume 42, number 2, pages 173-175, January, 1983.
When a semiconductor has subsidiary valleys in the conduction band, electrons can be driven from the primary valley to subsidiary valleys by light. The large difference in electron effective mass between the two valleys can then lead to a sizable optical nonlinearity. Kash's work has shown, however, that electrons are driven from one valley to another by optical heating, rather than by direct photon absorption. As a consequence, at room temperature the valley transfer nonlinearity is exceedingly weak in a material such as n-GaAs since, in it, carrier temperature modulation about 300 K is insufficient to excite carriers over the large barrier (.DELTA..perspectiveto.0.3 ev), between the .GAMMA. and L-valleys. Kash, in fact, could only observe a sizable valley transfer nonlinearity in n-GaAs when the samples were heated to 800 K. The material n-GaSb, with .DELTA..perspectiveto.0.08 ev, is much more favorable than n-GaAs in this regard. In it, Kash and Walrod (unpublished) have observed a large, room temperature nonlinearity (X.sup.3 .perspectiveto.10.sup.-6 esu) in experiments performed with CO.sub.2 lasers whose frequencies are well below the GaSb bandgap.
The scaling of the value of the valley transfer nonlinearity to a pump laser of shorter wavelength is governed by the variation of free carrier induced third order nonlinear susceptibility, X.sup.(3), with laser frequencies: ##EQU1##
where .omega..sub.1 .perspectiveto..omega..sub.2 .perspectiveto..omega..sub.3 are optical frequencies in a nonlinear mixing process.
In the absence of other effects one would anticipate from Kash's and Walrod's results, a X.sup.(3) in n-GaSb at 1.5.mu. of approximately 4.times.10.sup.-10 esu. It is well known, however, that optical processes in semiconductors are strongly enhanced (the solid state analogue of resonance fluorescence) as the laser frequency approaches a direct band gap, according to the formula: ##EQU2##
Previous experience suggests that this fact could enhance the near IR X.sup.(3) of GaSb to 4.times.10.sup.-8 esu, which is sizable.
Low absorption is also essential for the successful application of a nonlinearity. The moderate doping levels required to activate the valley-transfer process mean that the free carrier absorption will be fairly low, making valley transfer a particularly attractive mechanism for devices. At .lambda.=1.55.mu., the free carrier absorption coefficient is estimated to be 1 cm.sup.-1. Combining this value with the predicted X.sup.(3) of 4.times.10.sup.-8 and the measured relaxation time of 1 ps, gives a potential figure of merit [X.sup.(3) /.alpha.T] of 4.times.10.sup.4, which exceeds that of GaAs excitonic processes, that typically have figures of merit in the 10.sup.2 range. Of course if band gap resonance is used to increase X.sup.(3), there will be a corresponding increase in linear absorption. Thus, there will be a trade-off between a larger magnitude of nonlinearity and lower linear absorption.
Using a thermal theory of free-carrier-induced optical nonlinearities, Wolff and Auyang in an article entitled "Novel free-carrier-induced optical non-linearities of narrow-gap semiconductors" in Semicond. Sci. Technol, Vol. 5, pages S57-S67, 1990, predict a X.sup.(3) of the form ##EQU3##
where n.sub.o =index of refraction, .alpha.=free carrier absorption coefficient, .epsilon.=free carrier contribution to the dielectric function, c.sub.v is the electronic specific heat, .tau..sub.th the thermal relaxation time of the carriers, and Y the parameter modulated by carrier temperature fluctuations. For the valley-transfer process, Y is the density of electrons in the .GAMMA.-valley. At thermal equilibrium: ##EQU4##
where g.perspectiveto.60 is the ratio of state densities for the L and .GAMMA.-valleys, and .DELTA. the energy difference between them. Differentiation shows that ##EQU5## has its largest value when ##EQU6##
With g=60, Eq. (5) implies .beta..DELTA..perspectiveto.4, or .DELTA..perspectiveto.0.1 ev for optimal room temperature operation. The material n-GaSb, with .DELTA.=0.08 ev, comes very close to satisfying this condition. Combining all these results with the expression for free carrier absorption gives ##EQU7##
where it has been assumed that .DELTA..omega..tau..sub.th &lt;&lt;1. It should be noted that the form of X.sup.(3) in Eq. (5) is similar to that calculated for the nonparabolicity process, but with E.sub.G replaced by .DELTA.. This similarity can be understood by noting that both mechanisms rely upon the thermal excitation of electrons to states that have different characteristics from those at the band edge. As compared with nonparabolicity, the valley transfer process has 30.times. larger nonlinearity because a much smaller excitation energy (.DELTA.vs. E.sub.G) is required to produce a substantial mass change.
At wavelengths below its bandgap, GaSb is a nearly optimal material for the valley transfer process at room temperature. Unfortunately, however, its bandgap is too small for use in 1.55.mu. optical devices. The material n-GaSb is barely transparent to 1.55.mu. radiation at 4 K and becomes opaque with increasing temperature because its bandgap decreases to 0.73 ev (.lambda..sub.c =1.70.mu.) at 300 K, i.e. room temperature.